AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |
Back to Blog
Supertuxkart curve fit12/13/2023 ![]() I talk about the usefulness of the covariance matrix in my previous article, and won’t go into it further here. The curve_fit algorithm is fairly straightforward with several fundamental input options that returns only two output variables, the estimated parameter values and the estimated covariance matrix. Now that we have a set of test data to fit the model to, we will set the starting guess or initial parameter values for our fitting algorithms: ![]() This will result in a plot similar to this: # Plot the original signal and overlay the noisy signal to show the scale of the noise NoiseSamples = np.random.normal(size=len(y), scale=StdNoise) # Generate random noise sampled from a normal (Gaussian) distribution Y = fcn2minExpCos(x, Beta1, Beta2) # Generate the signal values before adding noise NumParams = 2 # Number of model parameters # Generate array of 101 data points from zero to ten in 0.1 incrementsīeta1 = 0.5 # First Beta parameter for the exponential decayīeta2 = 5 # Second Beta parameter for the cosine # Simulate data using the same function we will fit to. My launch.json file for the Python File debugging option section looks like this: Otherwise, VS Code will not step through any code but your own. When you have that, if you want to be able to step into the module fitting (Numpy, SciPy, etc.), you need to add the justM圜ode option and set it to false. This will create a launch.json file in your code directory. Note, when debugging Python in Visual Studio Code (VS Code), once you have the Python extension installed, follow these instructions to setup your debugging configuration. I performed all testing using Visual Studio Code with the installed Python extension. Python version was 3.8.1 (visible by typing “python –V” at the command prompt), SciPy version was 1.4.1, NumPy version was 1.18.1, and LMFit version was 1.0.0 (access module versions by printing/examining. Testing NotesĪll testing was performed locally on my personal PC running Windows 10. The last module we will look at is the LMFit module, a module designed specifically for NLLS Regression applications. ![]() The first two methods come from the popular scientific module SciPy, specifically its optimize submodule, curve_fit and least_squares. Rather, I’m going to discuss a few options available as Python modules, how to call these functions, and how to obtain or calculate certain return values. I won’t do as a complete explanation of the regression algorithm, what certain measures mean, and how to display them, as I did in my previous post. If you do have data with continuous variables, though, and after trying linear regression and polynomial regression, you still feel that you can fit your data better with some other nonlinear model, welcome to NLLS Regression! Now, if you have a lot of categorical variables or qualitative data, a classification algorithm such as logistic regression or other methods will work a lot better. We might only have two or three data dimensions/variables that we could measure. In many applications, however, we don’t have rich, multidimensional data sets, we might only have tens of data points. The same holds if you have access to millions of documents with billions and billions of words. If you have a dataset with millions of high-resolution, full-color images, of course you are going to want to use a deep neural network that can pick out all of the nuances. Have a bunch of data? Throw it into a neural network, train on your data, sit back with your feet up and a drink in your hand, gain all kinds of insights, something, something, PROFIT! Why use something antiquated like NLLS parametric regression where you have to specify your model and parameters, use a neural network instead (ignore that you have to choose what type of neural network to use, how many layers, how many neurons in each layer, what type of neurons, etc.)! I’m not going to argue that neural networks/deep learning aren’t amazing in what they can do in data science, but their power comes from two things: massive amounts of computing power and storage, and the explosion in the number and quantity of data. I wrote that walkthrough article a few years before this one, and since then, all nonlinear problems in data science seem to be immediately chucked into the magic answer machine called Deep Learning. In this article I will revisit my previous article on how to do Nonlinear Least Squares (NLLS) Regression fitting, but this time I will explore some of the options in the Python programming language. Nonlinear Least Squares Regression for Python
0 Comments
Read More
Leave a Reply. |